Title worksheet 2.1 - 2.6 questions.pdf ✅

Name ________________________________ AP Calculus AB Topics 2.1-2.4 Definition of the Derivative Part I. Multiple Choice Choose the best answer for each problem. Each problem is worth 2 points. You have 20 minutes. 1. The expression 0 ( ) ( ) lim x f x x f x   x     is sometimes presented as 0 ( ) ( ) lim h f a h f a  h   . Give the meaning of the expressions (i – iv) in Question 1 by choosing from the possibilities (A-I) below and writing the answer in the blank provided. Each expression has only one correct answer. Refer to the diagram to help you. (Each blank is worth 1⁄2 point.) i. f a h ( )  __________ ii. f a h f a ( ) ( )   __________ iii. f a h f a ( ) ( ) h   __________ iv. 0 ( ) ( ) lim h f a h f a  h   __________ (A) the y-value of Point P (B) the y-value of Point Q (C) the (horizontal) distance from a to a + h (D) the (vertical) distance from f (a) to f (a + h) (E) the (slant) distance from P to Q (F) the slope of the secant line at P (G) the slope of the secant line at Q (H) the slope of the secant line joining P and Q (I) the slope of the tangent line at P 2. The limit 2 0 (1 ) (1) lim x x   x     equals f c ( ) for some function, f x( ) , and some constant, c. Determine f x( ) and c. (A) 2 f x x c ( ) 1; 1    (B) f x x c ( ) ; 1    (C) 2 f x x c ( ) ; 1   (D) 2 f x x c ( ) ; 1   
3. In the figure to the right, the graph of the function f x( ) is shown. Arrange these values from smallest to largest. I. 1 (1) 4 3 4 f f        II.   1 ( ) 1 lim x 1 f x f  x   III. f f (2) (1)  (A) I, II, III (B) II, I, III (C) III, I, II (D) III, II, I (E) II, III, I 4. Let f x x ( ) 2   . Which of the following gives the correct limit definition of the derivative of f x( ) evaluated at x  6 ? (A) 2 2 2 '(6) 6 x f x     (B) 2 2 2 2 '(6) lim x 2 x f  x     (C) 6 2 2 2 '(6) lim x 6 x f  x     (D) 6 2 6 '(6) lim x 6 x f  x     5. The function shown at the right is differentiable at which of the following? (A) x 1 (B) x  2 (C) x  3 (D) x  2 and x  3 (E) x  0, x  3, and x  4 Part I. Multiple Choice Choose the best answer for each problem. Each problem is worth 2 points.
Name ________________________________ AP Calculus AB Topics 2.1-2.4 Definition of the Derivative You have 20 minutes. 1. The expression 0 ( ) ( ) lim x f x x f x   x     is sometimes presented as 0 ( ) ( ) lim h f a h f a  h   . Give the meaning of the expressions (i – iv) in Question 1 by choosing from the possibilities (A-I) below and writing the answer in the blank provided. Each expression has only one corrct answer. Refer to the diagram to help you. (Each blank is worth 1⁄2 point.) i. f a h ( )  __________ ii. f a h f a ( ) ( )   __________ iii. f a h f a ( ) ( ) h   __________ iv. 0 ( ) ( ) lim h f a h f a  h   __________ (A) the y-value of Point Q (B) the y-value of Point P (C) the (vertical) distance from f (a) to f (a + h) (D) the (horizontal) distance from a to a + h (E) the (slant) distance from P to Q (F) the slope of the secant line at Q (G) the slope of the secant line at P (H) the slope of the tangent line at P (I) the slope of the secant line joining P and Q 2. Let f x x ( ) 2   . Which of the following gives the correct limit definition of the derivative of f x( ) evaluated at x  6 ? (A) 6 2 2 2 '(6) lim x 6 x f  x     (B) 6 2 6 '(6) lim x 6 x f  x     (C) 2 2 2 2 '(6) lim x 2 x f  x     (D) 2 2 2 '(6) 6 x f x    
3. In the figure to the right, the graph of the function f x( ) is shown. Arrange these values from largest to smallest. I. 1 (1) 4 3 4 f f        II.   1 ( ) 1 lim x 1 f x f  x   III. f f (2) (1)  (A) III, I, II (B) I, II, III (C) II, III, I (D) II, I, III (E) III, II, I 4. The function shown at the right is differentiable at which of the following? (A) x  0, x  3, and x  4 (B) x 1 x  2 (C) x  3 (D) x  2 (E) x 1 5. The limit 2 0 (1 ) (1) lim x x   x     equals f c ( ) for some function, f x( ) , and some constant, c. Determine f x( ) and c. (A) 2 f x x c ( ) 1; 1    (B) 2 f x x c ( ) ; 1   (C) f x x c ( ) ; 1    (D) 2 f x x c ( ) ; 1   